Coefficient Variability Disks and Unified Fekete–Szego Inequalities for Filtered Janowski-Rotated Pseudo-Bazilević Functions

For 0≤α<1 and λ≥0, we introduce a filtered Janowski-rotated pseudo-Bazilević class of normalized analytic functions in the unit disk. The fractional power is defined through the unique analytic logarithm normalized at the origin, and a first-order differential filter is applied before the rotated Janowski subordination. Explicit formulae for a2 and a3 reduce the direct, logarithmic, inverse, and inverse-logarithmic Fekete–Szego-type functionals to a common Schwarz coefficient template. We derive a fixed-a2 variability disk for a3, Janowski disk containment, a positive-real-part consequence, and branch-free reconstruction formulae. Sharpness and function-level realization are unconditional on the integrable slice α=0. For 0<α<1, the variability disk is exact at the Schwarz-data level and is realized by a function whenever the explicitly reconstructed auxiliary function is nonvanishing. Numerical results, including a two-parameter surface, show the damping effect of λ on the base coefficient scales and on representative complete bounds while also displaying their interaction with α, the rotation, and the Janowski parameters.